The "wooden bomb" is actually rather large and divided into components that can be readily assembled into a functioning weapon. That's the first step in reducing the onerous maintenance on an atomic weapon, after all (e.g. reducing the radiation's deterioration of the electronics, the conventional explosives, etc.).Another step is that the "wooden bomb" is built such that the expected nuclear decay of the atomic trigger, booster, and case/shell only reduces its yield over time, but still allows it to be functional at least...for years.
But that ain't no tiny, lightweight suitcase bomb from the old Soviet Union!